Objective:
To represent operations on integers with positive and negative
charges.
Materials:
Overhead projector, drawing of an empty beaker on an acetate, bingo
chips (two colors needed).
Procedure:
The "positive-negative" model was used to represent addition
and subtraction, however, this model can also be extended to represent
division and multiplication.
To use this model the blue chips represent negative charges. The
red chips represent positive charges. The beaker represented on the
acetate will be used to combine the charges. We are not concerned
with individual charges, but with collection of charges in the beaker.
Therefore, an empty jar would have a collective charge of zero. If the
jar contains an equal number of blue and red chips, the charge is also
zero. Three positive (red) chips and three negative (blue) chips form
a 1:1 correspondence and they therefore cancel each other. The
collective charge of the beaker is zero.
AdditionEx. 1. +3+(4)=+7 Place three red chips in the beaker, add four red chips. The collective charge is now a positive seven. Ex. 2. -5+(2)=-3 Place five blue chips in the beaker then add two red chips. Match a blue and and red chip 1:1 until two sets of zeroes are matched. Remove the matched chips from the beaker. There are now three blue chips remaining in the beaker. The collective charge is now represented by as negative three. The answer -3 represented by the three blue chips. Subtraction
Ex. 3. -2-(+7)
Place two blue chips in the beaker. We now must create +7. Add
zeroes (seven red chips and seven blue chips), to the beaker. The
collective charge is -2. Now, remove the seven positive (red) charges.
Only blue (negative) chips remain. Your answer is represented by the
nine blue chips that remain.
Multiplication and division can be similarly represented.
A COMPLETE MODEL FOR OPERATIONS ON INTEGERS by Michael BattistaArithmetic Teacher, May 1983.